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The Handshaking Lemma (Graphs: Algorithms & Theory)

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First published at 17:56 UTC on September 12th, 2022.

Dr. Daniel R. Page

PageWizard Games, Learning & Entertainment

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A valuable concept in graph theory is the degree of a vertex, and the Handshaking Lemma. While we may revisit this topic further if there is interest, I wanted to introduce this cute but powerful concept to you. It is used often in explaining basic analysis techniques for algorithms, depending on the way the graph is represented, and sometimes in cute counting tricks!

In this video, we see how we could apply the Handshaking Lemma to figure out how many edges at most a simple graph can have and what a complete graph is!

Time Stamps:
0:00 Opening, definition of degree of a vertex
4:02 Handshaking Lemma and a proof
14:45 What is the maximum number of edges a simple graph can have? What is a complete graph. Application of Handshaking Lemma.
24:48 Closing

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